Preheat the oven to 375°F. Butter 10 muffin cups (or 12, for slightly smaller muffins) or line with paper liners.
Combine the flour, bran, baking powder, salt, and ground ginger in a large bowl and whisk to blend. Add the crystallized ginger, mix, and make a well.
In a separate bowl, whisk the egg until frothy. Add the applesauce, brown sugar, oil, milk, and molasses and whisk to blend. Pour into the well and stir with a wooden spoon until evenly blended.
Divide the batter evenly among the prepared cups.
Bake for 23 to 25 minutes, or until the muffins form domes that spring back when touched.
Transfer the pan to a cooling rack for 5 minutes, then remove the muffins from the pan and place on the rack until ready to serve.